雅克比迭代算法

#include <iostream>

#include <string>

#include <vector>

#include <iomanip>

using namespace std;

 

const int n=3;          //设置方程组的维

 

float a[n][n],x[n],b[n];

 

void input_data() //输入方程组的相关数据

{  

    cout<<"输入方程组的系数矩阵a["<<n<<"]["<<n<<"]:"<<endl;

    for(int i=0;i<n;i++)

        for(int j=0;j<n;j++)

            cin>>a[i][j];

    cout<<"输入x[1,...,"<<n<<"]的初值:"<<endl;

    for(i=0;i<n;i++)       

            cin>>x[i];

    cout<<"输入b[1,...,"<<n<<"]的初值:"<<endl;

    for(i=0;i<n;i++)       

            cin>>b[i]; 

}

 

void output_equation() //输出方程组

{

    for(int i=0;i<n;i++)

    {

        for(int j=0;j<n;j++)

        {

            if(j>0&&a[i][j]>0)

                cout<<"+";

            cout<<a[i][j]<<" x["<<j+1<<"] ";

        }

        cout<<"="<<b[i]<<endl;

    }

}

 

void main ()

{

    input_data();

    int counter;            //设置计算时迭代的次数

    cout<<"输入迭代的次数"<<endl;

    cin>>counter;

    system("cls");

    output_equation();

    int k=0,i=0;            //k用来统计迭代的次数;i用来表示x的序列

    float m_num1;     //m_x用来保存x的原先值;m_num1用来计算j!=i的数据之和

    cout<<endl;

    cout<<"k/t";

    for(int j=0;j<n;j++)

        cout<<"x["<<j+1<<"]/t/t/t";

    cout<<endl;

    cout<<k<<"/t";

    k++;

    cout << setiosflags(ios::fixed);   //和下一句结合起来用来设定小数位的位数

    cout << setprecision(10);

    float x_next[n];

    for(j=0;j<n;j++)

    {

        cout<<x[j]<<"/t/t";

    }

    cout<<endl;

    do

    {      

        m_num1=0;

        for(j=0;j<n;j++)

        {

            if(j!=i)

                m_num1=m_num1+a[i][j]*x[j];    

        }

        x_next[i]=(b[i]-m_num1)/a[i][i];       

        if(i<n-1)

            i++;

        else

        {

            for(j=0;j<n;j++)

                x[j]=x_next[j];

            cout<<k<<"/t";

            for(j=0;j<n;j++)

                cout<<x[j]<<"/t/t";

            cout<<endl;

            i=0;

            k++;

        };     

    }while(k<=counter);

}